This has nothing to do with what browser is used. The user is being redirected to the login page to accept some new ToS, instead of being automatically logged in. This would happen with any browser that supports redirects and cookies, and if for some reason the redirect didn't work, they'd just politely ask you to click on a certain link to continue (and if cookies are disabled, auto-login would not work).
If I understand the link's post correctly, the user is being logged out of his Google Chrome profile (which is used to save your browsing data across devices) and being redirected to the login page to accept some new ToS. Accepting that ToS for the browser setting set up his Google+ profile, it seems.
As far as I know, no other browser (IE,Firefox,Safari) has a social network (and very few actually nudge you into logging in to some profile when using it) and so this has a lot to do with what browser is used.
The author would likely not get this behaviour on any other browser (I'm on Firefox, I use some of Google's services and my Google+ account is still disabled), which is another reason to believe this has a lot to do with what browser is used.
